Abstract

We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. In accordance with economic models of risky human capital, we assume that dynamics of human capital is modeled as a multiplicative stochastic process which, in the long run, leads to the destruction of individual human capital. When agents are linked by fully redistributive taxation the situation might turn to individual growth in the long run. We consider that a government collects a proportion of income and reduces it by a fraction as costs for administration (efficiency losses). The remaining public good is equally redistributed to all agents. Sustainable growth is induced by redistribution despite the losses from the random growth process and despite administrative costs. Growth results from a portfolio effect. The findings are verified for three different tax schemes: proportional tax, taking proportionally more from the rich, and proportionally more from the poor. We discuss which of these tax schemes performs better with respect to maximize growth under a fixed rate of administrative costs, and the governmental income. This leads us to general conclusions about governmental decisions, the relation to public good games with free riding, and the function of taxation in a risk-taking society.

Abstract

We study a system in which N agents have to decide between two strategies θ_(i) (i ∈ 1... N), for defection or cooperation, when interacting with other n agents (either spatial neighbors or randomly chosen ones). After each round, they update their strategy responding nonlinearly to two different information sources: (i) the payoff a_(i)(θ_(i), f_(i)) received from the strategic interaction with their n counterparts, (ii) the fraction f_(i) of cooperators in this interaction. For the latter response, we assume social herding, i.e. agents adopt their strategy based on the frequencies of the different strategies in their neighborhood, without taking into account the consequences of this decision. We note that f_(i) already determines the payoff, so there is no additional information assumed. A parameter ζ defines to what level agents take the two different information sources into account. For the strategic interaction, we assume a Prisoner's Dilemma game, i.e. one in which defection is the evolutionary stable strategy. However, if the additional dimension of social herding is taken into account, we find instead a stable outcome where cooperators are the majority. By means of agent-based computer simulations and analytical investigations, we evaluate the critical conditions for this transition towards cooperation. We find that, in addition to a high degree of social herding, there has to be a nonlinear response to the fraction of cooperators. We argue that the transition to cooperation in our model is based on less information, i.e. on agents which are not informed about the payoff matrix, and therefore rely on just observing the strategy of others, to adopt it. By designing the right mechanisms to respond to this information, the transition to cooperation can be remarkably enhanced.

Abstract

In this paper we focus on diversity-induced resonance, which was recently found in bistable, excitable, and other physical systems. We study the appearance of this phenomenon in a purely economic model of cooperating and defecting agents. An agent's contribution to a public good is seen as a social norm, so defecting agents face a social pressure, which decreases if free riding becomes widespread. In this model, diversity among agents naturally appears because of the different sensitivities towards the social norm. We study the evolution of cooperation as a response to the social norm (i) for the replicator dynamics and (ii) for the logit dynamics by means of numerical simulations. Diversity-induced resonance is observed as a maximum in the response of agents to changes in the social norm as a function of the degree of heterogeneity in the population. We provide an analytical, mean-field approach for the logit dynamics and find very good agreement with the simulations. From a socioeconomic perspective, our results show that, counterintuitively, diversity in the individual sensitivity to social norms may result in a society that better follows such norms as a whole, even if part of the population is less prone to follow them.

Abstract

We consider a population of agents that are heterogeneous with respect to (i) their strategy when interacting ng times with other agents in an iterated prisoners dilemma game, (ii) their spatial location on K different islands. After each generation, agents adopt strategies proportional to their average payoff received. Assuming a mix of two cooperating and two defecting strategies, we first investigate for isolated islands the conditions for an exclusive domination of each of these strategies and their possible coexistence. This allows to define a threshold frequency for cooperation that, dependent on ng and the initial mix of strategies, describes the outbreak of cooperation in the absense of migration. We then allow migration of a fixed fraction of the population after each generation. Assuming a worst case scenario where all islands are occupied by defecting strategies, whereas only one island is occupied by cooperators at the threshold frequency, we determine the optimal migration rate that allows the outbreak of cooperation on all islands. We further find that the threshold frequency divided by the number of islands, i.e. the relative effort for invading defecting islands with cooperators decreases with the number of islands. We also show that there is only a small bandwidth of migration rates, to allow the outbreak of cooperation. Larger migration rates destroy cooperation.

Abstract

Wisdom of crowds refers to the phenomenon that the aggregate prediction or forecast of a group of individuals can be surprisingly more accurate than most individuals in the group, and sometimes - than any of the individuals comprising it. This article models the impact of social influence on the wisdom of crowds. We build a minimalistic representation of individuals as Brownian particles coupled by means of social influence. We demonstrate that the model can reproduce results of a previous empirical study. This allows us to draw more fundamental conclusions about the role of social influence: In particular, we show that the question of whether social influence has a positive or negative net effect on the wisdom of crowds is ill-defined. Instead, it is the starting configuration of the population, in terms of its diversity and accuracy, that directly determines how beneficial social influence actually is. The article further examines the scenarios under which social influence promotes or impairs the wisdom of crowds.

Abstract

Aging is always present, tailoring our interactions with others, and postulating a finite lifespan during which we are able to exercise them. We consider the prisoner’s dilemma game on a square lattice and examine how quenched age distributions and different aging protocols influence the evolution of cooperation when taking the life experience and knowledge accumulation into account as time passes. In agreement with previous studies, we find that a quenched assignment of age to players, introducing heterogeneity to the game, substantially promotes cooperative behavior. Introduction of aging and subsequent death as a coevolutionary process may act detrimental on cooperation but enhances it efficiently if the offspring of individuals that have successfully passed their strategy is considered newborn. We study resulting age distributions of players and show that the heterogeneity is vital—yet insufficient—for explaining the observed differences in cooperator abundance on the spatial grid. The unexpected increment of cooperation levels can be explained by a dynamical effect that has a highly selective impact on the propagation of cooperator and defector states.

Abstract

Experimental studies have shown the ubiquity of altruistic behavior in human societies. The social structure is a fundamental ingredient to understand the degree of altruism displayed by the members of a society, in contrast to individual-based features, like for example age or gender, which have been shown not to be relevant to determine the level of altruistic behavior. We explore an evolutionary model aiming to delve how altruistic behavior is affected by social structure. We investigate the dynamics of interacting individuals playing the Ultimatum Game with their neighbors given by a social network of interaction. We show that a population self-organizes in a critical state where the degree of altruism depends on the topology characterizing the social structure. In general, individuals offering large shares but in turn accepting large shares, are removed from the population. In heterogeneous social networks, individuals offering intermediate shares are strongly selected in contrast to random homogeneous networks where a broad range of offers, below a critical one, is similarly present in the population.

Abstract

In this paper, we present experimental investigations on a day-to-day route choice scenario. Here, the equilibrium outcome is, according to real traffic observations, fair (equal for all users) but induces an inefficient usage of network capacity. Optimal usage would be characterized by some users winning and some losing in comparison to the equilibrium state. Coherent alternating cooperation strategies can be a suitable solution but they require innovation and group coordination in addition to cooperativeness. In these points, our work differs considerably from other contributions observing the emergence of cooperation in social dilemmas. By classifying the two-person variant of our experiments among the symmetrical 2x2 games we show the situation of the Route Choice Game not to not addressed by the literature so far. Although the equilibrium outcome in this setup is “strongly stable”, in our experiments we find eminent empirical evidence of alternating cooperation and, thereby, observed persistent utilization of the system optimum that is not profitable for all individuals. The transition to this optimal configuration can be well described by quantitative considerations that are presented in the paper. Furthermore, the straight success of a learning scenario indicates that the collective innovation of alternating strategies may be the most critical challenge to the individuals instead of just learning to be cooperative. Presumably, this also holds for other social dilemma situations.

Abstract

We investigate the adaptation of cooperating strategies in an iterated Prisoner’s Dilemma (IPD) game. The deterministic IPD describes the interaction ofN agents spatially distributed on a lattice, which are assumed to only interact with their four neighbors, hence, local config-urations are of great importance. Particular interest is in the spatial-temporal distributions of agents playing different strategies, and their dependence on the number of consecutive en-counters ng during each generation.We show that above a critical ng, there is no coexistence between agents playing different strategies, while below the critical ng coexistence is found.

Abstract

We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally interacts with his neighbors. Based on a detailed analysis of the local payoff structures we derive critical conditions for the invasion or the spatial coexistence of cooperators and defectors. These results are concluded in a phase diagram that allows to identify five regimes, each characterized by a distinct spatiotemporal dynamics and a corresponding final spatial structure. In addition to the complete invasion of defectors, we find coexistence regimes with either a majority of cooperators in large spatial domains, or a minority of cooperators organized in small non-stationary domains or in small clusters. The analysis further allowed a verification of computer simulation results by Nowak and May (1993). Eventually, we present simulation results of a true 5-person game on a lattice. This modification leads to non-uniform spatial interactions that may even enhance the effect of cooperation. Keywords: Prisoner's dilemma; cooperation; spatial 5-person game